what's the probability that x^2+bx+c=0 has real root?

[tennis89]

can any one answer this one?

[Dason]

Do you know a condition on a,b,c that guarantee that there will be real roots?

Also: Do you have any other information about b and c? Do they need to positive? In a certain range? Are you assuming a certain distribution?

[tennis89]

yes.

we should have b^2>4c

so I want to find the ratio of area under y<x^2/4 in the real coordinate plane, which is the probability, but I have problem find the ratio of the area to the whole real domain

b, c can be any real value, I think we should assume uniform distribution here

[BGM]

uniform distribution should be only defined in a finite bounded interval.

If the support of b and c are the whole real line, you need other type of distribution to
model them. (e.g. normal)